几乎CAP~*-子群与有限群的p-超可解性  

Nearly CAP~*-Subgroups and p-Supersolvability of Finite Groups

作　　者：钟祥贵 孙悦 吴湘华 ZHONG Xianggui;SUN Yue;WU Xianghua(College of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China)

机构地区：[1]广西师范大学数学与统计学院

出　　处：《广西师范大学学报（自然科学版）》2019年第4期74-78,共5页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11261007);广西自然科学基金(2014GXNSFAA118009)

摘　　要：设G是有限群,子群H称为G的CAP^*-子群,如果H覆盖或者避开G的每个非-Frattini主因子。子群H称为G的几乎CAP^*-子群,如果存在G的次正规子群K使得HK=G,且H∩K是G的CAP^*-子群。本文应用G的某些素数幂阶几乎CAP^*-子群刻画有限群的p-超可解性,推广了相关文献的一些结果。A subgroup H of a finite group G is called a CAP^*-subgroup of G,if H either covers or avoids every non-Frattini chief factor of G.A subgroup H of G is said to be a nearly CAP^*-subgroup of G if there exists a subnormal subgroup K of G such that HK=G and H∩K is a CAP^*-subgroup of G.This paper investigates the structure of G under the assumption that certain subgroups of prime power orders are nearly CAP^*-subgroups of G,and a series of known results are generalized.

关 键 词：有限群 几乎CAP^*-子群 P-超可解群 

分 类 号：O152.1[理学—数学]